R-square

parameters mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
Rsq_0 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 7229.472 0.9996735
Rsq_1 0.6852229 0.0001198 0.0099777 0.6651230 0.6786501 0.6853013 0.6918406 0.7046081 6933.367 1.0009153
Rsq_2 0.7910192 0.0000838 0.0086723 0.7732616 0.7853215 0.7912014 0.7971278 0.8071652 10713.070 0.9996877
Rsq_3 0.7928579 0.0000806 0.0089157 0.7748120 0.7870419 0.7931025 0.7989407 0.8099293 12222.670 0.9999323
Rsq_4 0.7753898 0.0001283 0.0100313 0.7549820 0.7689504 0.7756084 0.7821284 0.7943110 6116.263 1.0001279
Rsq_4 0.7719234 0.0001201 0.0100096 0.7515610 0.7654170 0.7721949 0.7787398 0.7907603 6948.441 0.9997681

Loo-compare the models

##            elpd_diff se_diff
## model_3       0.0       0.0 
## model_2      -4.0       2.8 
## model_4     -28.9      10.2 
## model_4_ht  -29.5      12.9 
## model_0    -519.3      37.0 
## model_1    -787.3      32.7
      df_alpha |>
        ggplot(aes(x = a_model2, y = a_model3)) +
        geom_point() +
        theme_minimal() +
        theme(
         legend.title = element_blank(),
         plot.title = element_text(size = 15),
         axis.title.y = element_text(size = 15),
         axis.title.x = element_text(size = 15),
         axis.text.x = element_text(size = 13),
         axis.text.y = element_text(size = 13)
        ) +
        xlim(c(-15,1)) +
        ylim(c(-15,1)) +
        labs(title = "alpha comparisons") +
        xlab("Model 2 alphas") +
        ylab("Model 3 alphas") +
        geom_abline(intercept = 0, slope = 1)

      df_alpha |>
        ggplot(aes(x = a_model2, y = a_model4)) +
        geom_point() +
        theme_minimal() +
        theme(
         legend.title = element_blank(),
         plot.title = element_text(size = 15),
         axis.title.y = element_text(size = 15),
         axis.title.x = element_text(size = 15),
         axis.text.x = element_text(size = 13),
         axis.text.y = element_text(size = 13)
        ) +
        xlim(c(-15,1)) +
        ylim(c(-15,1)) +
        labs(title = "alpha comparisons") +
        xlab("Model 2 alphas") +
        ylab("Model 4 alphas") +
        geom_abline(intercept = 0, slope = 1)

      df_alpha |>
        ggplot(aes(x = a_model3, y = a_model4)) +
        geom_point() +
        theme_minimal() +
        theme(
         legend.title = element_blank(),
         plot.title = element_text(size = 15),
         axis.title.y = element_text(size = 15),
         axis.title.x = element_text(size = 15),
         axis.text.x = element_text(size = 13),
         axis.text.y = element_text(size = 13)
        ) +
        xlim(c(-15,1)) +
        ylim(c(-15,1)) +
        labs(title = "alpha comparisons") +
        xlab("Model 3 alphas") +
        ylab("Model 4 alphas") +
        geom_abline(intercept = 0, slope = 1)